Grocery Customer Segmentation

About this dataset :
Customer Personality Analysis is a detailed analysis of a company’s ideal customers. It helps a business to better understand its customers and makes it easier for them to modify products according to the specific needs, behaviors and concerns of different types of customers.

Customer personality analysis helps a business to modify its product based on its target customers from different types of customer segments. For example, instead of spending money to market a new product to every customer in the company’s database, a company can analyze which customer segment is most likely to buy the product and then market the product only on that particular segment.

Attributes

Customer Information

ID : Customer’s unique identifier
Year_Birth : Customer’s birth year
Education : Customer’s education level
Marital_Status: Customer’s marital status
Income : Customer’s yearly household income
Kidhome : Number of children in customer’s household
Teenhome : Number of teenagers in customer’s household
Dt_Customer : Date of customer’s enrollment with the company
Recency : Number of days since customer’s last purchase
Complain : 1 if the customer complained in the last 2 years, 0 otherwise

Products

MntWines : Amount spent on wine in last 2 years
MntFruits : Amount spent on fruits in last 2 years
MntMeatProducts : Amount spent on meat in last 2 years
MntFishProducts : Amount spent on fish in last 2 years
MntSweetProducts: Amount spent on sweets in last 2 years
MntGoldProds : Amount spent on gold in last 2 years

Promotion

NumDealsPurchases: Number of purchases made with a discount
AcceptedCmp1 : 1 if customer accepted the offer in the 1st campaign, 0 otherwise
AcceptedCmp2 : 1 if customer accepted the offer in the 2nd campaign, 0 otherwise
AcceptedCmp3 : 1 if customer accepted the offer in the 3rd campaign, 0 otherwise
AcceptedCmp4 : 1 if customer accepted the offer in the 4th campaign, 0 otherwise
AcceptedCmp5 : 1 if customer accepted the offer in the 5th campaign, 0 otherwise
Response : 1 if customer accepted the offer in the last campaign, 0 otherwise

Place

NumWebPurchases : Number of purchases made through the company’s website
NumCatalogPurchases: Number of purchases made using a catalogue
NumStorePurchases : Number of purchases made directly in stores
NumWebVisitsMonth : Number of visits to company’s website in the last month

Dataset Source: Kaggle : https://www.kaggle.com/imakash3011/customer-personality-analysis

1. Data Understanding

# Load libraries
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ ggplot2 3.3.5     ✓ purrr   0.3.4
## ✓ tibble  3.1.6     ✓ dplyr   1.0.7
## ✓ tidyr   1.1.4     ✓ stringr 1.4.0
## ✓ readr   2.1.1     ✓ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(corrplot)
## corrplot 0.92 loaded
library(gridExtra)
## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
library(GGally)
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(knitr)
library(ggplot2)

1.1. Load Data

# create a dataframe and store as variable df 
options(repr.matrix.max.cols=30, repr.matrix.max.rows=30) # to show all column
cust <- read.csv('marketing_campaign.csv')

# display top 6 first rows
head(cust)
##     ID Year_Birth  Education Marital_Status Income Kidhome Teenhome Dt_Customer
## 1 5524       1957 Graduation         Single  58138       0        0  04/09/2012
## 2 2174       1954 Graduation         Single  46344       1        1  08/03/2014
## 3 4141       1965 Graduation       Together  71613       0        0  21/08/2013
## 4 6182       1984 Graduation       Together  26646       1        0  10/02/2014
## 5 5324       1981        PhD        Married  58293       1        0  19/01/2014
## 6 7446       1967     Master       Together  62513       0        1  09/09/2013
##   Recency MntWines MntFruits MntMeatProducts MntFishProducts MntSweetProducts
## 1      58      635        88             546             172               88
## 2      38       11         1               6               2                1
## 3      26      426        49             127             111               21
## 4      26       11         4              20              10                3
## 5      94      173        43             118              46               27
## 6      16      520        42              98               0               42
##   MntGoldProds NumDealsPurchases NumWebPurchases NumCatalogPurchases
## 1           88                 3               8                  10
## 2            6                 2               1                   1
## 3           42                 1               8                   2
## 4            5                 2               2                   0
## 5           15                 5               5                   3
## 6           14                 2               6                   4
##   NumStorePurchases NumWebVisitsMonth AcceptedCmp3 AcceptedCmp4 AcceptedCmp5
## 1                 4                 7            0            0            0
## 2                 2                 5            0            0            0
## 3                10                 4            0            0            0
## 4                 4                 6            0            0            0
## 5                 6                 5            0            0            0
## 6                10                 6            0            0            0
##   AcceptedCmp1 AcceptedCmp2 Complain Response
## 1            0            0        0        1
## 2            0            0        0        0
## 3            0            0        0        0
## 4            0            0        0        0
## 5            0            0        0        0
## 6            0            0        0        0
# display bottom 6 last rows
tail(cust)
##         ID Year_Birth  Education Marital_Status Income Kidhome Teenhome
## 2235  8372       1974 Graduation        Married  34421       1        0
## 2236 10870       1967 Graduation        Married  61223       0        1
## 2237  4001       1946        PhD       Together  64014       2        1
## 2238  7270       1981 Graduation       Divorced  56981       0        0
## 2239  8235       1956     Master       Together  69245       0        1
## 2240  9405       1954        PhD        Married  52869       1        1
##      Dt_Customer Recency MntWines MntFruits MntMeatProducts MntFishProducts
## 2235  01/07/2013      81        3         3               7               6
## 2236  13/06/2013      46      709        43             182              42
## 2237  10/06/2014      56      406         0              30               0
## 2238  25/01/2014      91      908        48             217              32
## 2239  24/01/2014       8      428        30             214              80
## 2240  15/10/2012      40       84         3              61               2
##      MntSweetProducts MntGoldProds NumDealsPurchases NumWebPurchases
## 2235                2            9                 1               1
## 2236              118          247                 2               9
## 2237                0            8                 7               8
## 2238               12           24                 1               2
## 2239               30           61                 2               6
## 2240                1           21                 3               3
##      NumCatalogPurchases NumStorePurchases NumWebVisitsMonth AcceptedCmp3
## 2235                   0                 2                 7            0
## 2236                   3                 4                 5            0
## 2237                   2                 5                 7            0
## 2238                   3                13                 6            0
## 2239                   5                10                 3            0
## 2240                   1                 4                 7            0
##      AcceptedCmp4 AcceptedCmp5 AcceptedCmp1 AcceptedCmp2 Complain Response
## 2235            0            0            0            0        0        0
## 2236            0            0            0            0        0        0
## 2237            0            0            1            0        0        0
## 2238            1            0            0            0        0        0
## 2239            0            0            0            0        0        0
## 2240            0            0            0            0        0        1

1.2. Dataset General Information

str(cust)
## 'data.frame':    2240 obs. of  27 variables:
##  $ ID                 : int  5524 2174 4141 6182 5324 7446 965 6177 4855 5899 ...
##  $ Year_Birth         : int  1957 1954 1965 1984 1981 1967 1971 1985 1974 1950 ...
##  $ Education          : chr  "Graduation" "Graduation" "Graduation" "Graduation" ...
##  $ Marital_Status     : chr  "Single" "Single" "Together" "Together" ...
##  $ Income             : int  58138 46344 71613 26646 58293 62513 55635 33454 30351 5648 ...
##  $ Kidhome            : int  0 1 0 1 1 0 0 1 1 1 ...
##  $ Teenhome           : int  0 1 0 0 0 1 1 0 0 1 ...
##  $ Dt_Customer        : chr  "04/09/2012" "08/03/2014" "21/08/2013" "10/02/2014" ...
##  $ Recency            : int  58 38 26 26 94 16 34 32 19 68 ...
##  $ MntWines           : int  635 11 426 11 173 520 235 76 14 28 ...
##  $ MntFruits          : int  88 1 49 4 43 42 65 10 0 0 ...
##  $ MntMeatProducts    : int  546 6 127 20 118 98 164 56 24 6 ...
##  $ MntFishProducts    : int  172 2 111 10 46 0 50 3 3 1 ...
##  $ MntSweetProducts   : int  88 1 21 3 27 42 49 1 3 1 ...
##  $ MntGoldProds       : int  88 6 42 5 15 14 27 23 2 13 ...
##  $ NumDealsPurchases  : int  3 2 1 2 5 2 4 2 1 1 ...
##  $ NumWebPurchases    : int  8 1 8 2 5 6 7 4 3 1 ...
##  $ NumCatalogPurchases: int  10 1 2 0 3 4 3 0 0 0 ...
##  $ NumStorePurchases  : int  4 2 10 4 6 10 7 4 2 0 ...
##  $ NumWebVisitsMonth  : int  7 5 4 6 5 6 6 8 9 20 ...
##  $ AcceptedCmp3       : int  0 0 0 0 0 0 0 0 0 1 ...
##  $ AcceptedCmp4       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ AcceptedCmp5       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ AcceptedCmp1       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ AcceptedCmp2       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Complain           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Response           : int  1 0 0 0 0 0 0 0 1 0 ...

Summary : 1. The dataset contains 27 variables.
2. Variable Dt_Customer was supposed to in DateTime type.
3. There are 16 numerical variable, 11 categorical variables.
4. We can extract the age of the customer using variable Year_Birth.
5. We can create variable children from addition of Kidhome and Teenhome.
6. We can also create the total spend of the products that customers bought, through sum of product that they bought.
7. We can extract the total of the days since customer start shopping in the grocery

1.3. Descriptive Statistics

summary(cust)
##        ID          Year_Birth    Education         Marital_Status    
##  Min.   :    0   Min.   :1893   Length:2240        Length:2240       
##  1st Qu.: 2828   1st Qu.:1959   Class :character   Class :character  
##  Median : 5458   Median :1970   Mode  :character   Mode  :character  
##  Mean   : 5592   Mean   :1969                                        
##  3rd Qu.: 8428   3rd Qu.:1977                                        
##  Max.   :11191   Max.   :1996                                        
##                                                                      
##      Income          Kidhome          Teenhome      Dt_Customer       
##  Min.   :  1730   Min.   :0.0000   Min.   :0.0000   Length:2240       
##  1st Qu.: 35303   1st Qu.:0.0000   1st Qu.:0.0000   Class :character  
##  Median : 51382   Median :0.0000   Median :0.0000   Mode  :character  
##  Mean   : 52247   Mean   :0.4442   Mean   :0.5062                     
##  3rd Qu.: 68522   3rd Qu.:1.0000   3rd Qu.:1.0000                     
##  Max.   :666666   Max.   :2.0000   Max.   :2.0000                     
##  NA's   :24                                                           
##     Recency         MntWines         MntFruits     MntMeatProducts
##  Min.   : 0.00   Min.   :   0.00   Min.   :  0.0   Min.   :   0   
##  1st Qu.:24.00   1st Qu.:  23.75   1st Qu.:  1.0   1st Qu.:  16   
##  Median :49.00   Median : 173.50   Median :  8.0   Median :  67   
##  Mean   :49.11   Mean   : 303.94   Mean   : 26.3   Mean   : 167   
##  3rd Qu.:74.00   3rd Qu.: 504.25   3rd Qu.: 33.0   3rd Qu.: 232   
##  Max.   :99.00   Max.   :1493.00   Max.   :199.0   Max.   :1725   
##                                                                   
##  MntFishProducts  MntSweetProducts  MntGoldProds    NumDealsPurchases
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   : 0.000   
##  1st Qu.:  3.00   1st Qu.:  1.00   1st Qu.:  9.00   1st Qu.: 1.000   
##  Median : 12.00   Median :  8.00   Median : 24.00   Median : 2.000   
##  Mean   : 37.53   Mean   : 27.06   Mean   : 44.02   Mean   : 2.325   
##  3rd Qu.: 50.00   3rd Qu.: 33.00   3rd Qu.: 56.00   3rd Qu.: 3.000   
##  Max.   :259.00   Max.   :263.00   Max.   :362.00   Max.   :15.000   
##                                                                      
##  NumWebPurchases  NumCatalogPurchases NumStorePurchases NumWebVisitsMonth
##  Min.   : 0.000   Min.   : 0.000      Min.   : 0.00     Min.   : 0.000   
##  1st Qu.: 2.000   1st Qu.: 0.000      1st Qu.: 3.00     1st Qu.: 3.000   
##  Median : 4.000   Median : 2.000      Median : 5.00     Median : 6.000   
##  Mean   : 4.085   Mean   : 2.662      Mean   : 5.79     Mean   : 5.317   
##  3rd Qu.: 6.000   3rd Qu.: 4.000      3rd Qu.: 8.00     3rd Qu.: 7.000   
##  Max.   :27.000   Max.   :28.000      Max.   :13.00     Max.   :20.000   
##                                                                          
##   AcceptedCmp3      AcceptedCmp4      AcceptedCmp5      AcceptedCmp1    
##  Min.   :0.00000   Min.   :0.00000   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.00000   Median :0.00000   Median :0.00000  
##  Mean   :0.07277   Mean   :0.07455   Mean   :0.07277   Mean   :0.06429  
##  3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.00000   Max.   :1.00000   Max.   :1.00000  
##                                                                         
##   AcceptedCmp2        Complain           Response     
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.000000   Median :0.0000  
##  Mean   :0.01339   Mean   :0.009375   Mean   :0.1491  
##  3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:0.0000  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.0000  
## 

Summary : 1. Based on the summary above, there is a varible that contains 24 missing value in variable Income 2. And also the values from all varibles are not in the same scale, so they should be transformed into the same scale before performing the clustering.

# Check the unique element in variable Education
table(cust$Education)
## 
##   2n Cycle      Basic Graduation     Master        PhD 
##        203         54       1127        370        486
# Check the unique element in variable Marital Status
table(cust$Marital_Status)
## 
##   Absurd    Alone Divorced  Married   Single Together    Widow     YOLO 
##        2        3      232      864      480      580       77        2

Summary : We can derive the new varible from variable Eduation and Marital Status

2. Data Cleaning

2.1. Check and Treat Missing Values

Since the total of missing values are only around 1% of the data, we just drop it.

# check the total of missing values
sum(is.na(cust))
## [1] 24
# create a copy of original data 
cln <- data.frame(cust)
# remove missing values
cln <- na.omit(cln)
# Check after remove the missing value
sum(is.na(cln))
## [1] 0

2.2. Check and The outliers

# Boxplot for each Attribute  

# Subset the dataframe without categorical feature, feature ID and Dt_Customer
col_names <- colnames(cln[c(2,5:7,9:20)])

# create loop to plot boxplot
for (i in col_names){
    boxplot <- ggplot(cln, aes_string(y=i)) +
    geom_boxplot(fill="#69b3a2")
    print(boxplot)
}

# define function to check the outliers using IQR
FindOutliers <- function(data) {
  lowerq = quantile(data)[2]
  upperq = quantile(data)[4]
  iqr = upperq - lowerq #Or use IQR(data)
  # we identify extreme outliers
  extreme.threshold.upper = (iqr * 1.5) + upperq
  extreme.threshold.lower = lowerq - (iqr * 1.5)
  result <- which(data > extreme.threshold.upper | data < extreme.threshold.lower)
  length(result)}
apply(cln[c(2,5:7,9:20)], 2, FindOutliers)
##          Year_Birth              Income             Kidhome            Teenhome 
##                   3                   8                   0                   0 
##             Recency            MntWines           MntFruits     MntMeatProducts 
##                   0                  35                 246                 174 
##     MntFishProducts    MntSweetProducts        MntGoldProds   NumDealsPurchases 
##                 222                 246                 205                  84 
##     NumWebPurchases NumCatalogPurchases   NumStorePurchases   NumWebVisitsMonth 
##                   3                  23                   0                   8
# check summary after treat missing values
summary(cln)
##        ID          Year_Birth    Education         Marital_Status    
##  Min.   :    0   Min.   :1893   Length:2216        Length:2216       
##  1st Qu.: 2815   1st Qu.:1959   Class :character   Class :character  
##  Median : 5458   Median :1970   Mode  :character   Mode  :character  
##  Mean   : 5588   Mean   :1969                                        
##  3rd Qu.: 8422   3rd Qu.:1977                                        
##  Max.   :11191   Max.   :1996                                        
##      Income          Kidhome          Teenhome      Dt_Customer       
##  Min.   :  1730   Min.   :0.0000   Min.   :0.0000   Length:2216       
##  1st Qu.: 35303   1st Qu.:0.0000   1st Qu.:0.0000   Class :character  
##  Median : 51382   Median :0.0000   Median :0.0000   Mode  :character  
##  Mean   : 52247   Mean   :0.4418   Mean   :0.5054                     
##  3rd Qu.: 68522   3rd Qu.:1.0000   3rd Qu.:1.0000                     
##  Max.   :666666   Max.   :2.0000   Max.   :2.0000                     
##     Recency         MntWines        MntFruits      MntMeatProducts 
##  Min.   : 0.00   Min.   :   0.0   Min.   :  0.00   Min.   :   0.0  
##  1st Qu.:24.00   1st Qu.:  24.0   1st Qu.:  2.00   1st Qu.:  16.0  
##  Median :49.00   Median : 174.5   Median :  8.00   Median :  68.0  
##  Mean   :49.01   Mean   : 305.1   Mean   : 26.36   Mean   : 167.0  
##  3rd Qu.:74.00   3rd Qu.: 505.0   3rd Qu.: 33.00   3rd Qu.: 232.2  
##  Max.   :99.00   Max.   :1493.0   Max.   :199.00   Max.   :1725.0  
##  MntFishProducts  MntSweetProducts  MntGoldProds    NumDealsPurchases
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   : 0.000   
##  1st Qu.:  3.00   1st Qu.:  1.00   1st Qu.:  9.00   1st Qu.: 1.000   
##  Median : 12.00   Median :  8.00   Median : 24.50   Median : 2.000   
##  Mean   : 37.64   Mean   : 27.03   Mean   : 43.97   Mean   : 2.324   
##  3rd Qu.: 50.00   3rd Qu.: 33.00   3rd Qu.: 56.00   3rd Qu.: 3.000   
##  Max.   :259.00   Max.   :262.00   Max.   :321.00   Max.   :15.000   
##  NumWebPurchases  NumCatalogPurchases NumStorePurchases NumWebVisitsMonth
##  Min.   : 0.000   Min.   : 0.000      Min.   : 0.000    Min.   : 0.000   
##  1st Qu.: 2.000   1st Qu.: 0.000      1st Qu.: 3.000    1st Qu.: 3.000   
##  Median : 4.000   Median : 2.000      Median : 5.000    Median : 6.000   
##  Mean   : 4.085   Mean   : 2.671      Mean   : 5.801    Mean   : 5.319   
##  3rd Qu.: 6.000   3rd Qu.: 4.000      3rd Qu.: 8.000    3rd Qu.: 7.000   
##  Max.   :27.000   Max.   :28.000      Max.   :13.000    Max.   :20.000   
##   AcceptedCmp3      AcceptedCmp4      AcceptedCmp5     AcceptedCmp1    
##  Min.   :0.00000   Min.   :0.00000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.00000   Median :0.0000   Median :0.00000  
##  Mean   :0.07356   Mean   :0.07401   Mean   :0.0731   Mean   :0.06408  
##  3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.00000   Max.   :1.0000   Max.   :1.00000  
##   AcceptedCmp2        Complain           Response     
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.000000   Median :0.0000  
##  Mean   :0.01354   Mean   :0.009477   Mean   :0.1503  
##  3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:0.0000  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.0000

From the box plot, outliers calculation using IQR method, and the summary of data, we can identify that there are around 50% outliers in this data. But the outliers here are basically the natural value. It is possible if the customer buy many wines, fishe, and etc. However for the income of 666666 might be the error data. Furthermore, there are also some outliers in feature Year_birth, It might be possible to have age of above 100, but according to average of human life, it’s not make sense. So we are gonna treat the outliers in feature income and Year_birth through removing the outliers, since the outliers are only 11.

# Removing the outliers in feature income

# create a variale which contains Q1 & Q3
Q.inc <- quantile(cln$Income, probs=c(.25, .75), na.rm = FALSE)
# calculate IQR
IQR.inc <- IQR(cln$Income)

# find the cut-off ranges beyond which all data points are outliers.
ub.inc <- (IQR.inc * 1.5) + Q.inc[2]
lb.inc <- Q.inc[1] - (IQR.inc * 1.5)

# extract the part of dataframe which isn't included the outlier values
cln <- subset(cln, cln$Income > lb.inc & cln$Income < ub.inc)

# Removing the outliers in feature Year_Birth

# create a variale which contains Q1 & Q3
Q.yb <- quantile(cln$Year_Birth, probs=c(.25, .75), na.rm = FALSE)
# calculate IQR
IQR.yb <- IQR(cln$Year_Birth)

# find the cut-off ranges beyond which all data points are outliers.
ub.yb <- (IQR.yb * 1.5) + Q.yb[2]
lb.yb <- Q.yb[1] - (IQR.yb * 1.5)

# extract the part of dataframe which isn't included the outlier values
cln <- subset(cln, cln$Year_Birth > lb.yb & cln$Year_Birth < ub.yb)
# Check the outlier in feature Income and Year_Birth after remove it
apply(cln[c(2,5)], 2, FindOutliers)
## Year_Birth     Income 
##          0          0

We can see that no outliers exist. It works !

3. Feature Engineering

After we finish clean the data, now there are some possibility to derive the new features from the existing features.

  1. Extract the “Age” of a customer by the “Year_Birth” indicating the birth year of the respective person.
  2. Create another feature “Total_Spent” indicating the total amount spent by the customer in various categories over the span of two years.
  3. Grouping similar value of “Marital_Status” to reduce the cardinality.
  4. Grouping similar value of “Education” to reduce the cardinality.
  5. Create a feature “Children” with combining the feature Kidhome and Teenhome
  6. Dropping some of the redundant features
# Extract the age of the customer
cln$Age <- 2022 - cln$Year_Birth

# Derive spent variable
cln$Total_Spent <- cln$MntFishProducts + cln$MntFruits + cln$MntGoldProds + cln$MntMeatProducts + cln$MntSweetProducts + cln$MntWines

# Derive variable total children in the family
cln$children <- cln$Kidhome + cln$Teenhome

# replace the value of some columns

# Education
cln$Education[cln$Education == "2n Cycle"] <- "undergraduate"
cln$Education[cln$Education == "Basic"] <- "undergraduate"
cln$Education[cln$Education == "Graduation"] <- "postgraduate"
cln$Education[cln$Education == "Master"] <- "postgraduate"
cln$Education[cln$Education == "PhD"] <- "postgraduate"

# Marital Status
cln$Marital_Status[cln$Marital_Status == "single"] <- "Single"
cln$Marital_Status[cln$Marital_Status == "Absurd"] <- "Single"
cln$Marital_Status[cln$Marital_Status == "Alone"] <- "Single"
cln$Marital_Status[cln$Marital_Status == "Together"] <- "Married"
cln$Marital_Status[cln$Marital_Status == "Widow"] <- "Divorced"
cln$Marital_Status[cln$Marital_Status == "YOLO"] <- "Single"
# change some columns' name
names(cln)[names(cln) == "MntWines"] <- "Wines"
names(cln)[names(cln) == "MntFruits"] <- "Fruits"
names(cln)[names(cln) == "MntSweetProducts"] <- "Sweet"
names(cln)[names(cln) == "MntMeatProducts"] <- "Meat"
names(cln)[names(cln) == "MntGoldProds"] <- "Gold"
names(cln)[names(cln) == "MntFishProducts"] <- "Fish"
names(cln)
##  [1] "ID"                  "Year_Birth"          "Education"          
##  [4] "Marital_Status"      "Income"              "Kidhome"            
##  [7] "Teenhome"            "Dt_Customer"         "Recency"            
## [10] "Wines"               "Fruits"              "Meat"               
## [13] "Fish"                "Sweet"               "Gold"               
## [16] "NumDealsPurchases"   "NumWebPurchases"     "NumCatalogPurchases"
## [19] "NumStorePurchases"   "NumWebVisitsMonth"   "AcceptedCmp3"       
## [22] "AcceptedCmp4"        "AcceptedCmp5"        "AcceptedCmp1"       
## [25] "AcceptedCmp2"        "Complain"            "Response"           
## [28] "Age"                 "Total_Spent"         "children"
# FIX DATASET 
clean_fe <- cln[, c("Age","Education","Marital_Status","children","Income","Recency","Wines","Fruits","Meat","Fish","Sweet","Gold",
                  "Total_Spent","NumDealsPurchases","NumWebPurchases","NumCatalogPurchases","NumStorePurchases","NumWebVisitsMonth",
                  "AcceptedCmp3","AcceptedCmp4","AcceptedCmp5","AcceptedCmp1","AcceptedCmp2","Complain","Response")]

# change all columns' name to lower case letter
names(clean_fe)<- tolower(names(clean_fe))
summary(clean_fe)
##       age        education         marital_status        children     
##  Min.   :26.0   Length:2205        Length:2205        Min.   :0.0000  
##  1st Qu.:45.0   Class :character   Class :character   1st Qu.:0.0000  
##  Median :52.0   Mode  :character   Mode  :character   Median :1.0000  
##  Mean   :53.1                                         Mean   :0.9488  
##  3rd Qu.:63.0                                         3rd Qu.:1.0000  
##  Max.   :82.0                                         Max.   :3.0000  
##      income          recency          wines            fruits     
##  Min.   :  1730   Min.   : 0.00   Min.   :   0.0   Min.   :  0.0  
##  1st Qu.: 35196   1st Qu.:24.00   1st Qu.:  24.0   1st Qu.:  2.0  
##  Median : 51287   Median :49.00   Median : 178.0   Median :  8.0  
##  Mean   : 51622   Mean   :49.01   Mean   : 306.2   Mean   : 26.4  
##  3rd Qu.: 68281   3rd Qu.:74.00   3rd Qu.: 507.0   3rd Qu.: 33.0  
##  Max.   :113734   Max.   :99.00   Max.   :1493.0   Max.   :199.0  
##       meat             fish            sweet             gold       
##  Min.   :   0.0   Min.   :  0.00   Min.   :  0.00   Min.   :  0.00  
##  1st Qu.:  16.0   1st Qu.:  3.00   1st Qu.:  1.00   1st Qu.:  9.00  
##  Median :  68.0   Median : 12.00   Median :  8.00   Median : 25.00  
##  Mean   : 165.3   Mean   : 37.76   Mean   : 27.13   Mean   : 44.06  
##  3rd Qu.: 232.0   3rd Qu.: 50.00   3rd Qu.: 34.00   3rd Qu.: 56.00  
##  Max.   :1725.0   Max.   :259.00   Max.   :262.00   Max.   :321.00  
##   total_spent     numdealspurchases numwebpurchases  numcatalogpurchases
##  Min.   :   5.0   Min.   : 0.000    Min.   : 0.000   Min.   : 0.000     
##  1st Qu.:  69.0   1st Qu.: 1.000    1st Qu.: 2.000   1st Qu.: 0.000     
##  Median : 397.0   Median : 2.000    Median : 4.000   Median : 2.000     
##  Mean   : 606.8   Mean   : 2.318    Mean   : 4.101   Mean   : 2.645     
##  3rd Qu.:1047.0   3rd Qu.: 3.000    3rd Qu.: 6.000   3rd Qu.: 4.000     
##  Max.   :2525.0   Max.   :15.000    Max.   :27.000   Max.   :28.000     
##  numstorepurchases numwebvisitsmonth  acceptedcmp3      acceptedcmp4    
##  Min.   : 0.000    Min.   : 0.000    Min.   :0.00000   Min.   :0.00000  
##  1st Qu.: 3.000    1st Qu.: 3.000    1st Qu.:0.00000   1st Qu.:0.00000  
##  Median : 5.000    Median : 6.000    Median :0.00000   Median :0.00000  
##  Mean   : 5.824    Mean   : 5.337    Mean   :0.07392   Mean   :0.07438  
##  3rd Qu.: 8.000    3rd Qu.: 7.000    3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :13.000    Max.   :20.000    Max.   :1.00000   Max.   :1.00000  
##   acceptedcmp5      acceptedcmp1     acceptedcmp2        complain      
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.0000   Median :0.00000   Median :0.00000  
##  Mean   :0.07302   Mean   :0.0644   Mean   :0.01361   Mean   :0.00907  
##  3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.0000   Max.   :1.00000   Max.   :1.00000  
##     response    
##  Min.   :0.000  
##  1st Qu.:0.000  
##  Median :0.000  
##  Mean   :0.151  
##  3rd Qu.:0.000  
##  Max.   :1.000

4. Visualization The Data

# Group the feature based on data type to ease the visualization

# numerical data
nums <- clean_fe[, c("age","children","income","recency","wines","fruits","meat","fish","sweet","gold","total_spent",
                "numdealspurchases","numwebpurchases","numcatalogpurchases","numstorepurchases","numwebvisitsmonth",
                "acceptedcmp3","acceptedcmp4","acceptedcmp5","acceptedcmp1","acceptedcmp2","complain","response")]

#categorical data
cats <- clean_fe[, c("education","marital_status")]

4.1. Density Plot

# Density plot for each attribute
col_nums <- colnames(nums)

for (i in col_nums){
    density <- ggplot(nums, aes_string(x=i)) +
    geom_density(fill="#69b3a2")
    print(density)
}

4.2. Correlation Plot

# load package
library(corrplot)
# create correlation plot
corr <- cor(nums)
corrplot(corr, type="upper", method="ellipse", tl.cex=0.9)

# Check the unique element in variable Marital Status
table(clean_fe$marital_status)
## 
## Divorced  Married   Single 
##      306     1422      477
# Check the unique element in variable Education
table(clean_fe$education)
## 
##  postgraduate undergraduate 
##          1953           252
head(clean_fe)
##   age    education marital_status children income recency wines fruits meat
## 1  65 postgraduate         Single        0  58138      58   635     88  546
## 2  68 postgraduate         Single        2  46344      38    11      1    6
## 3  57 postgraduate        Married        0  71613      26   426     49  127
## 4  38 postgraduate        Married        1  26646      26    11      4   20
## 5  41 postgraduate        Married        1  58293      94   173     43  118
## 6  55 postgraduate        Married        1  62513      16   520     42   98
##   fish sweet gold total_spent numdealspurchases numwebpurchases
## 1  172    88   88        1617                 3               8
## 2    2     1    6          27                 2               1
## 3  111    21   42         776                 1               8
## 4   10     3    5          53                 2               2
## 5   46    27   15         422                 5               5
## 6    0    42   14         716                 2               6
##   numcatalogpurchases numstorepurchases numwebvisitsmonth acceptedcmp3
## 1                  10                 4                 7            0
## 2                   1                 2                 5            0
## 3                   2                10                 4            0
## 4                   0                 4                 6            0
## 5                   3                 6                 5            0
## 6                   4                10                 6            0
##   acceptedcmp4 acceptedcmp5 acceptedcmp1 acceptedcmp2 complain response
## 1            0            0            0            0        0        1
## 2            0            0            0            0        0        0
## 3            0            0            0            0        0        0
## 4            0            0            0            0        0        0
## 5            0            0            0            0        0        0
## 6            0            0            0            0        0        0

5. Data Pre-Processing

In this section, we will perform some data pre-processing methods to prepare the data for modeling
1. Label encoding for categorical faetures 2. Scaling the features

5.1. Label Encoding

# import the library for label encoding
library(superml)
## Loading required package: R6
# Encoding for Feature Education

# LabelEncoder$new() creates and initializes an instance of the Label Encoder class.
label <- LabelEncoder$new()
# LabelEncoder$fit() create memory space for the encoding values but it does not return any value as an output.
print(label$fit(clean_fe$education))
## [1] TRUE
# LabelEncoder$fit_transform() encode the data as well as reserve memory for the encoding values ahead.
clean_fe$education <- label$fit_transform(clean_fe$education)
# print the result
print(clean_fe$education)
##    [1] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
##   [38] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
##   [75] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0
##  [112] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0
##  [149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0
##  [186] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
##  [223] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [260] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
##  [297] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
##  [334] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
##  [371] 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
##  [408] 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0
##  [445] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
##  [482] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
##  [519] 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
##  [556] 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
##  [593] 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [630] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0
##  [667] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
##  [704] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
##  [741] 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
##  [778] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1
##  [815] 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0
##  [852] 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [889] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1
##  [926] 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0
##  [963] 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [1000] 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0
## [1037] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1074] 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1
## [1111] 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## [1148] 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0
## [1185] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## [1222] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [1259] 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0
## [1296] 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
## [1333] 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1
## [1370] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0
## [1407] 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1444] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
## [1481] 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0
## [1518] 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1555] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
## [1592] 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
## [1629] 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1666] 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
## [1703] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1
## [1740] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0
## [1777] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## [1814] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1
## [1851] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [1888] 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1925] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
## [1962] 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
## [1999] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## [2036] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
## [2073] 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [2110] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [2147] 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0
## [2184] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
# Encoding for Feature marital_status

# LabelEncoder$fit() create memory space for the encoding values but it does not return any value as an output.
print(label$fit(clean_fe$marital_status))
## [1] TRUE
# LabelEncoder$fit_transform() encode the data as well as reserve memory for the encoding values ahead.
clean_fe$marital_status <- label$fit_transform(clean_fe$marital_status)
# print the result
print(clean_fe$marital_status)
##    [1] 0 0 1 1 1 1 2 1 1 1 1 2 2 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 2 1 1 2 1 0 1 1 2
##   [38] 2 1 1 1 1 0 1 1 1 2 1 0 2 1 1 2 0 1 0 1 0 2 1 1 1 0 1 1 1 1 1 1 2 1 0 1 1
##   [75] 0 1 1 1 2 1 1 0 1 1 0 1 1 2 2 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1
##  [112] 1 0 1 2 0 1 0 1 1 1 0 1 1 1 2 1 0 2 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1
##  [149] 0 0 1 1 2 1 2 2 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
##  [186] 1 0 2 0 2 1 0 0 1 2 1 2 1 1 1 1 1 1 0 1 2 1 1 1 1 1 2 1 1 2 1 1 0 2 1 0 1
##  [223] 1 1 0 0 2 1 0 1 1 1 1 1 1 1 0 0 2 1 1 0 1 0 0 0 2 2 1 1 1 1 1 1 1 1 0 0 1
##  [260] 1 2 1 0 1 0 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 0 2 2 1 1 0 1 1 2 0 1 1
##  [297] 2 1 0 1 1 1 0 1 1 1 2 2 0 1 2 1 1 0 0 0 1 1 1 2 2 1 1 0 2 1 1 1 2 1 2 2 1
##  [334] 1 1 0 1 0 0 1 1 1 1 1 2 1 1 1 0 1 2 1 0 1 1 0 0 0 0 0 0 1 0 1 1 2 1 0 0 1
##  [371] 1 1 2 1 1 0 1 1 1 1 1 0 1 2 1 0 1 0 1 0 2 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1
##  [408] 1 1 1 1 1 1 0 1 1 1 0 1 2 2 1 1 1 1 1 0 1 2 2 0 1 1 0 1 0 1 1 1 0 1 1 1 1
##  [445] 2 2 1 1 0 1 2 1 1 1 1 1 1 0 1 0 1 1 1 1 2 0 1 1 2 1 1 1 2 1 2 1 0 2 2 2 1
##  [482] 1 1 1 1 1 1 1 2 1 0 1 2 1 0 1 1 1 0 1 0 1 1 2 0 1 1 1 1 1 1 0 1 2 0 1 1 0
##  [519] 1 1 2 1 0 1 2 0 1 1 1 2 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 2 1 0 1 0 1 1 1
##  [556] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 0 1 0 1 1 1 2 1 1 1 0 1 0 1 1 0 2 2 1
##  [593] 1 0 2 1 1 0 1 0 2 1 1 0 2 0 1 1 0 1 2 0 1 1 1 0 0 2 0 1 2 1 1 1 2 0 1 1 1
##  [630] 2 1 1 0 1 1 1 2 1 1 1 0 1 1 2 1 1 1 1 0 1 1 1 0 2 1 0 1 1 0 1 0 2 2 1 1 1
##  [667] 2 0 1 1 2 0 1 1 2 1 0 0 0 1 2 1 2 0 2 1 2 2 1 1 1 0 0 1 1 1 2 1 2 0 1 1 1
##  [704] 1 1 1 1 2 1 1 2 1 1 2 2 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 2 1 1 1 1 1 1 1
##  [741] 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 2 1 2 1 1 0 1 0 0 1
##  [778] 2 1 1 1 2 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 2 1 2 2 1 2 0 1 1
##  [815] 1 1 0 2 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1
##  [852] 0 1 0 1 1 2 1 0 1 0 1 2 1 0 1 0 1 1 0 1 2 1 0 2 0 1 2 1 2 1 2 1 1 1 0 0 2
##  [889] 1 1 0 1 2 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 2 0 1 2 1 0
##  [926] 1 1 2 1 2 1 1 2 0 1 1 1 0 1 2 2 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2
##  [963] 2 2 1 1 1 1 0 2 2 1 1 0 2 0 1 1 1 2 2 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1
## [1000] 0 1 1 1 1 1 1 0 0 2 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 2 1 0
## [1037] 1 1 0 1 1 1 0 2 1 1 0 2 2 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1
## [1074] 0 1 0 2 0 1 1 2 1 1 1 1 0 1 1 1 1 2 0 0 0 0 1 1 1 1 1 0 1 2 0 1 2 0 1 0 2
## [1111] 1 0 1 1 0 1 1 2 2 1 1 1 2 0 2 1 1 1 1 0 2 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
## [1148] 1 1 0 1 1 1 1 1 1 1 1 2 0 1 1 2 0 0 0 1 0 1 1 2 2 2 0 1 2 1 1 1 2 1 1 1 2
## [1185] 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 2 1 2 1 0 1 1 1 2 1 2 1 1 1 1 1 1 0 0
## [1222] 1 0 1 1 2 0 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 0 2 1 1 1 0 1 0 0 1 2 1 1 1
## [1259] 2 1 1 2 1 1 1 2 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 2 1 1 1 1 1 1 1 0 1 1 1 0
## [1296] 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 2 0 1 1 1 1 0 0 1 1 1 2 1 0 1
## [1333] 1 1 0 1 0 0 0 1 1 2 1 2 0 0 1 2 1 0 1 0 2 1 0 0 1 1 2 1 1 1 1 1 1 1 1 1 0
## [1370] 1 1 2 2 2 1 1 1 1 0 1 1 1 1 1 2 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1
## [1407] 2 1 0 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 0 0 1 1 2 1 0 1 2 1 1 1 1 2 1 1
## [1444] 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 0
## [1481] 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 2 1 0 1 1 1 1 0 1 0 0 2 1 0 1 1
## [1518] 1 0 2 1 1 0 2 1 2 1 1 1 1 1 1 2 2 2 1 1 1 2 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1
## [1555] 0 1 1 2 1 2 2 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 2 1 1 1 1 0 1 1 0 1 0 0 1 1
## [1592] 1 0 1 1 1 1 1 0 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 0 2 2 1 0 2
## [1629] 2 0 1 1 1 0 0 1 2 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 2 1 0 0 0
## [1666] 2 1 0 1 2 1 1 2 2 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 2 0 0 1 0
## [1703] 1 1 1 1 2 1 0 2 0 1 1 1 1 1 0 1 2 1 1 1 2 1 1 1 0 2 2 0 1 0 1 1 1 2 1 1 1
## [1740] 1 0 1 1 1 2 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1
## [1777] 1 0 1 1 0 0 1 0 1 0 1 1 2 1 1 0 1 1 1 2 0 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 1
## [1814] 2 1 2 2 1 1 1 1 1 1 0 0 1 1 1 0 2 0 1 1 1 1 2 0 1 1 2 1 0 1 1 2 2 0 0 2 0
## [1851] 2 1 1 2 1 1 2 0 0 0 1 2 1 1 1 1 1 2 0 2 1 0 0 1 1 0 1 2 1 1 1 1 1 1 1 0 1
## [1888] 1 2 0 1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 2 1 1 1 1 0 1 1 2 1 1 0 1
## [1925] 0 1 0 1 0 2 1 0 0 2 1 2 1 0 2 1 1 1 2 1 2 0 1 1 1 1 1 0 1 0 1 2 1 1 0 1 1
## [1962] 1 1 1 2 1 0 0 1 1 1 1 1 0 0 2 1 0 0 1 1 2 2 1 2 0 1 1 0 1 1 1 2 1 1 1 1 1
## [1999] 1 1 1 2 1 1 2 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 2 0 1 0 2 2 1 1 1
## [2036] 1 1 2 1 1 1 1 1 1 1 0 1 2 1 2 1 1 1 1 1 1 0 1 2 1 1 0 1 1 1 0 1 1 1 1 1 1
## [2073] 1 1 1 2 1 0 2 1 1 1 1 1 1 1 0 2 1 1 1 1 1 1 1 1 1 1 2 0 1 0 1 2 0 2 2 2 1
## [2110] 2 1 0 0 1 1 1 1 1 1 1 2 1 1 2 1 1 0 1 1 1 2 0 0 2 0 1 0 0 2 1 1 1 1 2 0 1
## [2147] 1 1 1 1 0 1 1 1 1 1 1 0 2 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 2 2 1 2 0 1 1
## [2184] 1 2 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 1 2 1 1
head(clean_fe)
##   age education marital_status children income recency wines fruits meat fish
## 1  65         0              0        0  58138      58   635     88  546  172
## 2  68         0              0        2  46344      38    11      1    6    2
## 3  57         0              1        0  71613      26   426     49  127  111
## 4  38         0              1        1  26646      26    11      4   20   10
## 5  41         0              1        1  58293      94   173     43  118   46
## 6  55         0              1        1  62513      16   520     42   98    0
##   sweet gold total_spent numdealspurchases numwebpurchases numcatalogpurchases
## 1    88   88        1617                 3               8                  10
## 2     1    6          27                 2               1                   1
## 3    21   42         776                 1               8                   2
## 4     3    5          53                 2               2                   0
## 5    27   15         422                 5               5                   3
## 6    42   14         716                 2               6                   4
##   numstorepurchases numwebvisitsmonth acceptedcmp3 acceptedcmp4 acceptedcmp5
## 1                 4                 7            0            0            0
## 2                 2                 5            0            0            0
## 3                10                 4            0            0            0
## 4                 4                 6            0            0            0
## 5                 6                 5            0            0            0
## 6                10                 6            0            0            0
##   acceptedcmp1 acceptedcmp2 complain response
## 1            0            0        0        1
## 2            0            0        0        0
## 3            0            0        0        0
## 4            0            0        0        0
## 5            0            0        0        0
## 6            0            0        0        0

5.2. Normalize data using range

Before applying the clustering, we have to normalize the features to be in the same range of values.

#load package
library(caret)
## Loading required package: lattice
## 
## Attaching package: 'caret'
## The following object is masked from 'package:purrr':
## 
##     lift
# Normalization
clean_fe_norm <-  data.frame(clean_fe)

# calculate the pre-process parameters from the dataset
preprocessParams <- preProcess(clean_fe_norm, method=c("range"))
# summarize transform parameters
print(preprocessParams)
## Created from 2205 samples and 25 variables
## 
## Pre-processing:
##   - ignored (0)
##   - re-scaling to [0, 1] (25)
# transform the dataset using the parameters
clean_fe_norm <- predict(preprocessParams, clean_fe_norm)
# summarize the transformed dataset
summary(clean_fe_norm)
##       age           education      marital_status      children     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.3393   1st Qu.:0.0000   1st Qu.:0.5000   1st Qu.:0.0000  
##  Median :0.4643   Median :0.0000   Median :0.5000   Median :0.3333  
##  Mean   :0.4839   Mean   :0.1143   Mean   :0.4612   Mean   :0.3163  
##  3rd Qu.:0.6607   3rd Qu.:0.0000   3rd Qu.:0.5000   3rd Qu.:0.3333  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##      income          recency           wines             fruits       
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.2988   1st Qu.:0.2424   1st Qu.:0.01607   1st Qu.:0.01005  
##  Median :0.4425   Median :0.4949   Median :0.11922   Median :0.04020  
##  Mean   :0.4454   Mean   :0.4950   Mean   :0.20507   Mean   :0.13268  
##  3rd Qu.:0.5942   3rd Qu.:0.7475   3rd Qu.:0.33958   3rd Qu.:0.16583  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.00000  
##       meat               fish             sweet               gold        
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.009275   1st Qu.:0.01158   1st Qu.:0.003817   1st Qu.:0.02804  
##  Median :0.039420   Median :0.04633   Median :0.030534   Median :0.07788  
##  Mean   :0.095833   Mean   :0.14578   Mean   :0.103543   Mean   :0.13725  
##  3rd Qu.:0.134493   3rd Qu.:0.19305   3rd Qu.:0.129771   3rd Qu.:0.17445  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.000000   Max.   :1.00000  
##   total_spent     numdealspurchases numwebpurchases   numcatalogpurchases
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.00000   Min.   :0.00000    
##  1st Qu.:0.0254   1st Qu.:0.06667   1st Qu.:0.07407   1st Qu.:0.00000    
##  Median :0.1556   Median :0.13333   Median :0.14815   Median :0.07143    
##  Mean   :0.2388   Mean   :0.15456   Mean   :0.15188   Mean   :0.09448    
##  3rd Qu.:0.4135   3rd Qu.:0.20000   3rd Qu.:0.22222   3rd Qu.:0.14286    
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.00000   Max.   :1.00000    
##  numstorepurchases numwebvisitsmonth  acceptedcmp3      acceptedcmp4    
##  Min.   :0.0000    Min.   :0.0000    Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.2308    1st Qu.:0.1500    1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :0.3846    Median :0.3000    Median :0.00000   Median :0.00000  
##  Mean   :0.4480    Mean   :0.2668    Mean   :0.07392   Mean   :0.07438  
##  3rd Qu.:0.6154    3rd Qu.:0.3500    3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :1.0000    Max.   :1.0000    Max.   :1.00000   Max.   :1.00000  
##   acceptedcmp5      acceptedcmp1     acceptedcmp2        complain      
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.0000   Median :0.00000   Median :0.00000  
##  Mean   :0.07302   Mean   :0.0644   Mean   :0.01361   Mean   :0.00907  
##  3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.0000   Max.   :1.00000   Max.   :1.00000  
##     response    
##  Min.   :0.000  
##  1st Qu.:0.000  
##  Median :0.000  
##  Mean   :0.151  
##  3rd Qu.:0.000  
##  Max.   :1.000

5.3. PCA

pca_df <- data.frame(clean_fe)
pca <- prcomp(pca_df, scale. = TRUE)
# Plot variance ration in each PCA 
pca_var <- pca$sdev^2
pca_var_perc <- round(pca_var/sum(pca_var) * 100, 1)
barplot(pca_var_perc, main = "Variation Plot", xlab = "PCs", ylab = "Percentage Variance", ylim = c(0, 100))

The barchart above shows that around 30% of the variation in the data is shown by PC1 and then very little is captured by the rest of the PCs. The most important features can be extract using rotation.

# Which features do contribute the most in PC1
PC1 <- pca$rotation[,1]
PC1_scores <- abs(PC1)
PC1_scores_ordered <- sort(PC1_scores, decreasing = TRUE)
names(PC1_scores_ordered)
##  [1] "total_spent"         "income"              "numcatalogpurchases"
##  [4] "meat"                "wines"               "numstorepurchases"  
##  [7] "fish"                "sweet"               "fruits"             
## [10] "numwebvisitsmonth"   "children"            "gold"               
## [13] "numwebpurchases"     "acceptedcmp5"        "acceptedcmp1"       
## [16] "response"            "acceptedcmp4"        "numdealspurchases"  
## [19] "acceptedcmp2"        "age"                 "education"          
## [22] "acceptedcmp3"        "complain"            "marital_status"     
## [25] "recency"

The top 2 features are total_spent and income. So we will select these features to build the K-means model.

6. K-Means Clustering Model

6.1. Find the optimal K using Elbow Plot

To study graphically which value of k gives us the best partition, we can plot betweenss and tot.withinss vs Choice of k.

bss <- numeric()
wss <- numeric()

# Run the algorithm for different values of k 
set.seed(1234)

# set range of k value from 1 to 10
for(i in 1:10){

  # For each k, calculate betweenss and tot.withinss
  bss[i] <- kmeans(clean_fe_norm[c(5,13)], centers=i)$betweenss
  wss[i] <- kmeans(clean_fe_norm[c(5,13)], centers=i)$tot.withinss

}

# Between-cluster sum of squares vs Choice of k
p3 <- qplot(1:10, bss, geom=c("point", "line"), 
            xlab="Number of clusters", ylab="Between-cluster sum of squares") +
  scale_x_continuous(breaks=seq(0, 10, 1)) +
  theme_bw()

# Total within-cluster sum of squares vs Choice of k
p4 <- qplot(1:10, wss, geom=c("point", "line"),
            xlab="Number of clusters", ylab="Total within-cluster sum of squares") +
  scale_x_continuous(breaks=seq(0, 10, 1)) +
  theme_bw()

# Subplot
grid.arrange(p3, p4, ncol=2)

From the elbow plot above, it’s clear that the optimal number of cluster = 3. After K = 3, the difference between BCSS and WCSS value are not significant.

6.2. Kmeans Modeling with Selected Features

# Execution of k-means with k=3
set.seed(1234)

cust_k3 <- kmeans(clean_fe_norm[c(5,13)], centers=3, nstart = 20)
cust_k3
## K-means clustering with 3 clusters of sizes 635, 445, 1125
## 
## Cluster means:
##      income total_spent
## 1 0.5474790  0.30843020
## 2 0.6770414  0.62246032
## 3 0.2962515  0.04777425
## 
## Clustering vector:
##    1    2    3    4    5    6    7    8    9   10   12   13   14   15   16   17 
##    2    3    1    3    1    1    1    3    3    3    3    1    1    3    2    3 
##   18   19   20   21   22   23   24   25   26   27   29   30   31   32   33   34 
##    3    2    3    3    1    1    1    3    3    3    3    2    3    3    3    3 
##   35   36   37   38   39   40   41   42   43   45   46   47   48   50   51   52 
##    2    3    1    3    3    1    2    3    3    3    1    3    3    2    1    2 
##   53   54   55   56   57   58   60   61   62   63   64   65   66   67   68   69 
##    3    2    1    2    1    3    1    2    1    1    1    1    3    3    2    1 
##   70   71   73   74   75   76   77   78   79   80   81   82   83   84   85   86 
##    2    2    1    1    3    3    2    2    3    1    3    3    3    3    1    3 
##   87   88   89   90   94   95   96   97   98   99  100  101  102  103  104  105 
##    3    3    2    3    3    3    3    1    3    1    3    3    3    2    1    2 
##  106  107  108  109  110  111  112  113  114  115  116  117  118  119  120  121 
##    3    3    1    3    1    1    2    1    1    3    3    2    3    3    3    1 
##  122  123  124  125  126  127  128  130  131  132  133  135  136  137  138  139 
##    3    3    3    2    1    2    3    1    1    1    1    3    2    3    3    3 
##  140  141  142  143  144  145  146  147  148  149  150  151  152  153  154  155 
##    3    2    1    2    1    3    1    3    3    3    3    1    1    3    3    1 
##  156  157  158  159  160  161  162  163  164  166  167  168  169  170  171  172 
##    2    3    3    3    2    3    2    3    2    3    1    3    1    3    3    3 
##  173  174  175  176  177  178  179  180  181  182  183  184  185  186  187  188 
##    3    3    3    2    2    3    3    1    3    3    1    3    3    3    3    1 
##  189  190  191  192  194  195  196  197  198  199  200  201  202  203  204  205 
##    2    3    3    2    3    3    3    1    2    2    3    1    2    1    2    3 
##  206  207  208  209  210  211  212  213  214  215  216  217  218  219  220  221 
##    3    3    3    3    2    3    1    3    1    2    3    3    2    3    1    3 
##  222  223  224  225  226  227  228  229  230  231  232  233  234  235  236  237 
##    1    1    3    2    3    1    1    2    3    3    2    3    3    1    3    3 
##  238  239  241  242  243  244  245  246  247  248  249  250  251  252  253  254 
##    1    3    2    1    3    2    1    3    2    2    2    2    3    3    2    3 
##  255  256  257  258  259  260  261  262  263  264  265  266  267  268  269  270 
##    2    3    1    3    3    3    3    1    3    3    3    3    2    3    1    3 
##  271  272  273  274  275  276  277  278  279  280  281  282  283  284  285  286 
##    2    3    1    3    3    1    1    1    1    1    3    1    3    1    3    3 
##  287  288  289  290  291  292  293  294  295  296  297  298  299  300  301  302 
##    1    1    2    3    3    3    2    3    3    2    3    3    1    1    3    1 
##  303  304  305  306  307  308  309  310  311  312  314  315  316  317  318  319 
##    3    3    3    2    3    2    1    3    3    3    2    3    3    3    1    3 
##  321  322  323  324  325  326  327  328  329  330  331  332  333  334  335  336 
##    1    3    3    2    3    2    3    3    3    3    3    3    1    3    3    1 
##  337  338  339  341  342  343  344  345  346  347  348  349  350  351  352  353 
##    2    3    2    2    3    1    1    3    1    3    2    3    3    1    2    1 
##  354  355  356  357  358  359  360  361  362  363  364  365  366  367  368  369 
##    2    2    3    3    2    1    3    2    1    3    3    1    1    2    3    2 
##  370  371  372  373  374  375  376  377  378  379  380  381  382  383  384  385 
##    1    3    3    3    2    3    3    3    3    2    3    3    3    3    3    3 
##  386  387  388  389  390  391  392  393  394  395  396  397  398  399  400  401 
##    3    3    1    3    2    2    1    1    3    1    2    3    3    3    3    3 
##  402  403  404  405  406  407  408  409  410  411  412  413  414  415  416  417 
##    1    3    3    1    3    3    1    3    1    3    1    2    3    1    2    3 
##  418  419  420  421  422  423  424  425  426  427  428  429  430  431  432  433 
##    2    2    1    3    3    3    2    2    3    2    2    3    1    2    1    1 
##  434  435  436  437  438  439  440  441  442  443  444  445  446  447  448  449 
##    1    3    3    1    1    3    3    3    3    3    3    3    3    3    2    3 
##  450  451  452  453  454  455  456  457  458  459  460  461  462  463  464  465 
##    1    1    1    3    1    1    3    2    3    3    2    1    1    3    2    3 
##  466  467  468  469  470  471  472  473  474  475  476  477  478  479  480  481 
##    2    2    3    1    1    2    3    1    3    3    1    3    1    1    3    3 
##  482  483  484  485  486  487  488  489  490  491  492  493  494  495  496  497 
##    3    3    3    1    1    1    1    3    3    2    3    2    1    1    1    3 
##  498  499  500  501  502  503  504  505  506  507  508  509  510  511  512  513 
##    2    1    1    3    3    3    2    3    1    1    2    3    1    3    1    3 
##  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528  529 
##    2    3    2    3    3    1    2    3    2    3    2    3    3    2    1    2 
##  530  531  532  533  534  535  536  537  538  539  540  541  542  543  544  545 
##    3    1    2    1    1    3    3    3    1    3    3    3    3    3    2    1 
##  546  547  548  549  550  551  552  553  554  555  556  557  558  559  560  561 
##    3    2    3    3    3    3    3    1    3    1    3    1    2    3    2    3 
##  562  563  564  565  566  567  568  569  570  571  572  573  574  575  576  577 
##    2    1    1    3    3    1    3    3    3    3    3    3    1    3    1    3 
##  578  579  580  581  582  583  584  585  586  587  588  589  590  591  592  593 
##    3    3    3    3    3    3    3    3    3    2    1    1    3    3    2    2 
##  594  595  596  597  598  599  600  601  602  603  604  605  606  607  608  609 
##    3    1    3    3    3    3    3    3    1    1    1    3    3    3    3    3 
##  610  611  612  613  614  615  616  617  619  620  621  622  623  624  625  626 
##    2    3    3    3    3    1    3    3    3    3    1    3    1    3    1    3 
##  627  628  629  630  631  632  633  634  635  636  637  638  639  640  641  642 
##    2    2    3    3    2    1    1    3    2    3    2    1    2    2    1    2 
##  643  644  645  646  647  648  649  650  651  652  653  654  655  657  658  659 
##    2    3    2    3    2    3    1    1    2    3    1    3    3    3    3    1 
##  660  661  662  663  664  665  666  667  668  669  670  671  672  673  674  675 
##    3    1    3    1    3    3    3    3    3    3    3    1    1    1    1    1 
##  676  677  678  679  680  681  682  683  684  685  686  687  689  690  691  692 
##    3    2    1    3    1    1    2    3    3    1    1    2    2    1    1    1 
##  693  694  695  696  697  698  699  700  701  702  703  704  705  706  707  708 
##    3    3    3    3    3    3    1    1    1    1    2    2    3    2    3    1 
##  709  710  711  712  713  714  715  716  717  718  719  720  721  722  723  724 
##    1    3    3    1    3    1    3    2    2    3    1    3    1    1    3    2 
##  725  726  727  728  729  730  731  732  733  734  735  736  737  738  739  740 
##    3    3    2    1    1    1    3    1    1    3    2    2    2    1    3    2 
##  741  742  743  744  745  746  747  748  749  750  751  752  753  754  755  756 
##    1    3    3    3    1    2    3    1    3    1    2    1    1    2    2    1 
##  757  758  759  760  761  762  763  764  765  766  767  768  769  770  771  772 
##    1    1    3    3    3    1    2    3    1    3    2    2    3    1    1    2 
##  773  774  775  776  777  778  779  780  781  782  783  784  785  786  787  788 
##    1    3    3    3    3    2    3    2    2    3    3    3    3    3    3    1 
##  789  790  791  792  793  794  795  796  797  798  799  800  801  802  803  804 
##    1    3    2    1    3    3    3    3    1    1    2    3    1    3    3    2 
##  805  806  807  808  809  810  811  812  813  814  815  816  817  818  819  820 
##    2    1    3    1    1    2    3    3    1    1    2    1    3    3    1    3 
##  821  822  823  824  825  826  827  828  829  830  831  832  833  834  835  836 
##    2    3    1    3    2    2    2    3    2    3    3    1    1    3    3    1 
##  837  838  839  840  841  842  843  844  845  846  847  848  849  850  851  852 
##    3    2    3    1    3    3    3    3    2    2    2    1    3    3    3    1 
##  853  854  855  856  857  858  859  860  861  862  863  864  865  866  867  868 
##    2    3    3    1    3    1    3    2    3    3    3    3    3    1    3    3 
##  869  870  871  872  873  874  875  876  877  878  879  880  881  882  883  884 
##    1    3    2    1    3    3    1    2    1    3    2    3    3    3    3    3 
##  885  886  887  888  889  890  891  892  893  894  895  896  897  898  899  900 
##    2    2    3    3    1    2    3    3    1    3    1    1    1    2    3    3 
##  901  902  903  904  905  906  907  908  909  910  911  912  913  914  915  916 
##    1    3    1    1    1    2    2    3    3    3    2    2    1    3    2    1 
##  917  918  919  920  921  922  923  924  925  926  927  928  929  930  931  932 
##    1    2    3    2    3    2    3    3    2    3    2    2    1    2    2    3 
##  933  934  935  936  937  938  939  940  941  942  943  944  945  946  947  948 
##    1    3    1    3    1    2    1    1    1    1    2    2    3    1    1    1 
##  949  950  951  952  953  954  955  956  957  958  959  960  961  962  963  964 
##    3    1    3    3    3    3    3    3    1    1    3    1    1    1    3    3 
##  965  966  967  968  969  970  971  972  973  974  975  976  977  978  979  980 
##    3    1    2    3    3    1    2    3    3    1    2    1    2    1    3    1 
##  981  982  983  984  985  986  987  988  989  990  991  992  993  994  995  996 
##    3    3    3    1    2    1    2    2    2    3    2    3    3    1    3    3 
##  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 
##    2    3    1    3    1    2    1    3    3    3    1    2    3    3    2    3 
## 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 
##    3    3    3    1    2    3    3    3    3    3    2    3    3    1    3    3 
## 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 
##    3    2    2    2    1    3    2    3    3    3    3    1    1    3    3    1 
## 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 
##    3    3    3    2    3    1    2    3    2    3    3    1    3    3    2    1 
## 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 
##    1    1    1    3    1    3    2    2    3    1    3    2    1    3    3    2 
## 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 
##    2    3    3    3    1    3    2    3    2    1    3    1    3    2    2    3 
## 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 
##    1    3    3    1    1    1    3    1    2    1    3    3    3    2    3    3 
## 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 
##    1    1    2    2    3    2    3    2    3    3    3    1    1    3    3    3 
## 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 
##    3    3    2    3    3    1    1    3    3    2    2    3    3    2    3    3 
## 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 
##    1    3    3    3    1    3    3    1    1    3    1    2    3    2    3    3 
## 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 
##    3    1    2    1    3    1    1    1    3    1    3    3    1    2    3    3 
## 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 
##    2    1    3    3    3    1    3    2    1    3    1    3    3    3    3    1 
## 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 
##    3    3    2    2    3    3    3    1    3    1    1    1    3    1    3    3 
## 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 
##    1    1    2    3    3    3    3    1    1    2    1    3    1    3    2    3 
## 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 
##    3    3    1    3    3    2    1    3    1    3    3    3    3    3    3    1 
## 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 
##    3    2    3    3    3    3    1    1    3    3    3    3    3    1    2    1 
## 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 
##    2    1    1    1    1    1    3    2    3    2    2    3    3    2    1    3 
## 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 
##    3    2    1    1    3    1    3    2    3    3    2    3    2    1    3    3 
## 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 
##    3    3    1    3    2    1    3    3    3    3    3    3    3    1    2    3 
## 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 
##    2    3    3    2    1    3    2    1    1    1    2    3    1    1    3    3 
## 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 
##    3    3    3    2    3    2    3    3    2    3    3    3    2    3    3    2 
## 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 
##    2    1    3    1    3    3    3    3    3    1    3    3    3    3    3    1 
## 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 
##    2    2    2    3    1    2    1    3    1    2    3    1    3    1    1    1 
## 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1381 1382 
##    2    3    3    3    1    3    3    3    1    1    3    1    3    1    3    3 
## 1385 1386 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 
##    3    2    3    3    2    3    3    3    3    3    1    3    3    1    1    1 
## 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 
##    1    3    3    1    3    3    1    1    3    1    2    3    2    3    1    3 
## 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 
##    3    3    3    3    1    2    3    3    3    3    3    3    3    3    3    2 
## 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 
##    3    1    3    1    3    3    3    3    3    3    2    2    3    2    1    2 
## 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 
##    1    3    2    2    3    3    1    3    3    2    3    1    1    3    3    3 
## 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 
##    1    1    2    3    2    3    3    3    2    1    3    2    3    3    1    1 
## 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 
##    1    3    3    2    1    2    1    2    3    1    3    2    1    3    1    3 
## 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 
##    1    2    2    1    3    3    1    2    1    1    1    1    1    2    3    2 
## 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 
##    2    3    3    1    3    3    3    2    2    3    3    3    1    2    3    2 
## 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 
##    3    2    3    1    3    3    3    3    1    1    1    3    1    2    3    1 
## 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 
##    3    3    3    1    3    3    1    1    1    1    3    3    3    3    1    3 
## 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 
##    1    3    1    3    3    2    1    1    1    2    3    2    3    3    3    3 
## 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 
##    2    3    1    3    1    1    3    1    3    3    1    3    2    3    1    3 
## 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 
##    3    3    3    3    3    2    3    1    2    2    3    3    3    1    1    1 
## 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 
##    1    2    3    2    3    3    1    3    1    1    1    3    3    2    1    3 
## 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 
##    3    1    3    3    3    1    3    3    3    3    1    1    1    3    3    3 
## 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1655 1656 1657 1658 
##    2    1    3    1    3    1    1    1    3    3    2    3    3    3    3    1 
## 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 
##    1    2    1    3    1    3    3    3    1    3    2    2    3    2    2    1 
## 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 
##    2    3    3    3    3    3    2    3    3    3    3    3    2    1    1    2 
## 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 
##    1    2    3    3    3    1    3    1    3    2    1    3    3    1    3    3 
## 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 
##    1    3    1    3    2    2    3    2    3    3    1    3    3    1    3    2 
## 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 
##    2    2    3    3    3    3    1    2    3    3    3    2    1    2    1    2 
## 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 
##    1    3    3    3    3    2    1    2    3    1    1    2    1    3    3    1 
## 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 
##    3    3    3    3    3    1    1    3    1    1    3    1    3    1    3    3 
## 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 
##    3    3    1    2    3    3    3    3    3    1    3    3    2    1    3    3 
## 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 
##    1    3    1    1    3    3    2    3    3    3    1    3    1    1    2    2 
## 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 
##    3    3    3    1    3    3    2    2    3    1    1    2    2    3    1    2 
## 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 
##    1    3    1    3    3    1    1    3    1    2    2    3    3    3    1    3 
## 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 
##    3    3    1    3    1    2    3    1    3    1    1    1    3    3    1    3 
## 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 
##    2    3    2    2    2    2    3    3    2    1    1    3    1    1    2    1 
## 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 
##    3    3    3    2    3    1    3    1    3    3    1    2    1    2    2    3 
## 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 
##    3    1    3    1    3    2    1    3    2    2    3    1    1    3    3    2 
## 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 
##    1    1    3    3    1    3    3    1    1    3    3    3    2    2    2    2 
## 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 
##    1    1    3    3    3    3    3    1    2    2    2    3    1    2    2    1 
## 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 
##    3    1    3    3    1    3    1    1    3    3    2    3    3    1    3    2 
## 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 
##    1    1    3    3    3    1    2    2    1    2    3    3    2    3    1    2 
## 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 
##    3    3    3    2    1    2    2    2    1    3    3    3    3    3    3    3 
## 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 
##    3    3    3    3    2    3    1    3    3    3    3    1    2    3    2    2 
## 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 
##    3    1    1    1    3    1    3    3    3    3    3    3    2    3    1    1 
## 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 
##    2    3    2    1    2    3    3    3    3    3    3    3    3    2    2    3 
## 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 
##    3    3    1    3    1    1    3    1    3    1    1    1    3    2    1    2 
## 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 
##    3    3    3    3    3    1    2    2    3    1    1    3    3    3    2    1 
## 2059 2061 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 
##    1    3    2    3    1    1    3    2    3    3    1    1    3    1    2    1 
## 2077 2078 2081 2083 2084 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 
##    3    3    3    1    2    1    1    2    3    3    1    3    1    2    1    3 
## 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 
##    2    3    2    2    3    1    3    2    3    3    3    1    3    2    1    1 
## 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 
##    3    3    3    1    3    1    2    3    3    3    3    1    3    2    1    2 
## 2129 2130 2131 2132 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 
##    2    3    3    2    3    1    1    3    3    1    3    3    3    3    3    1 
## 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 
##    2    3    3    1    3    3    2    3    3    3    3    3    3    1    1    2 
## 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 
##    1    3    2    3    3    2    2    2    3    1    1    1    2    1    2    2 
## 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 
##    3    1    3    3    3    3    3    3    1    1    2    1    3    2    3    3 
## 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 
##    2    2    3    3    1    1    3    3    1    3    1    3    3    1    3    3 
## 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 
##    3    3    2    3    2    3    3    3    2    3    3    1    2    3    3    1 
## 2226 2227 2228 2230 2231 2232 2233 2235 2236 2237 2238 2239 2240 
##    1    1    1    3    3    1    3    3    2    1    1    1    3 
## 
## Within cluster sum of squares by cluster:
## [1] 11.377367  9.548749 14.938724
##  (between_SS / total_SS =  82.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

Additionally, the kmeans() function returns some ratios that let us know how compact is a cluster and how different are several clusters among themselves.

  1. betweenss. The between-cluster sum of squares. In an optimal segmentation, one expects this ratio to be as higher as possible, since we would like to have heterogeneous clusters.

  2. withinss. Vector of within-cluster sum of squares, one component per cluster. In an optimal segmentation, one expects this ratio to be as lower as possible for each cluster, since we would like to have homogeneity within the clusters.

  3. tot.withinss. Total within-cluster sum of squares.

  4. totss. The total sum of squares

A good clustering has a small WSS(k) and a large BSS(k).

# Between-cluster sum of squares
cust_k3$betweenss
## [1] 165.1532
# Within-cluster sum of squares
cust_k3$withinss
## [1] 11.377367  9.548749 14.938724
# Total within-cluster sum of squares / inertia value
cust_k3$tot.withinss
## [1] 35.86484

6.3. Cluster Interpretation

#Plot the data to see the clusters:
cust_k3$cluster <- as.factor(cust_k3$cluster)
ggplot(clean_fe, aes(income, total_spent, color = cust_k3$cluster)) + geom_point()

The bigger income of the customers, the more the total expenses.